Quote:
Originally Posted by whosnext
Suppose you are told the optimal probs for Game A. Now you get to play Game B. Since Game B is identical to Game A except you get 11 points rather than 10 points in some situations, isn't it clear that you should want to play 11 more often than you played 10?
If you are still not convinced, why don't you write down the payouts to Player 1 if he plays H, M, or L (high, mid, low) given the choices of Player 2 and Player 3. Then write down the expected value of each choice for Player 1.
I still dont think it matters, your not seeking to maximise your EV, but simply score more points (player with most points wins). Perhaps you are seeking to maximise your EV, but your EV doesnt depend on the size of the numbers but simply 1pt for winning a game and 0 for not winning.
from what I posted before;
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if we compare two games; choices in game X= [1000,100,1] , choices in game Y = [10,8,7]
in both X and Y if you choose the top pay off you only win if neither player chooses top
in both X and Y if you choose middle you only win if both players choose the same (as long as they both dont pick middle)
in both X and Y if you choose smallest you only win if both players choose the same (as long as they both dont pick smallest)
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if the choices are just [high, med, low], you still win in the same manner as above.
The ways in which you can win are identical, it doesnt matter if the winner has 10pts or 1000pts, a win is a win.
if you then considered the game where choices are [10^10000000,1.1,1], your EV method would assign almost 100% to choosing the biggest number, if I knew two players were doing that it would be pretty simple to exploit.
Last edited by akkopower1; 02-21-2017 at 01:33 AM.